I have an upstairs room with an HVAC vent in the ceiling above the door. The return air is in the hallway just outside of the same door. This room also happens to be the hottest room in the house (by 5-10 degrees in the afternoon). I'm wondering if the duct location is incorrect? My theory is that the cold air is immediately sucked out of the room and never displaces the warm air in the room. Would moving the duct to the other side of the room make a difference in this case?
Make sure you're adjusting the vents in the other room so that the coolest rooms receive the least air from the HVAC. Then, as a quick and easy test, try installing a vent deflector that attaches with magnets to push the cool air across the ceiling and into the room, rather than blowing straight down and out the door.
I'm not a HVAC engineer, but your reasoning and theory sound good and well thought out to me.
I strongly believe (until I'm proven wrong) that moving the vent to the other side of the room would make a (noticeable) difference to the room's overall temperature during the warmer months.
Does the same duct-work heat your home during the winter months?
If yes, you will also want to take that into account when repositioning the vent.